A Case Study in Dimensional Deconstruction

We test Arkani-Hamed et al.'s dimensional deconstruction on a model that is predicted to have a naturally light composite Higgs boson, i.e., one whose mass M is much less than its binding scale \Lambda, and whose quartic coupling \lambda is large, so that its vacuum expectation value v \sim M/\sqrt{\lambda} << \Lambda also. We consider two different underlying dynamics--UV completions--at the scale \Lambda for this model. We find that the expectation from dimensional deconstruction is not realized and that low energy details depend crucially on the UV completion. In one case, M << \Lambda and \lambda << 1, hence, v \sim \Lambda. In the other, \lambda can be large or small, but then so is M, and v is still O(\Lambda).